The work done against friction can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be expressed as:
work = ΔKE = 1/2 * m * (vf^2 - vi^2)
where m is the mass of the car, vi is the initial velocity, and vf is the final velocity.
Plugging in the given values, we get:
work = 1/2 * 500 kg * (20 m/s)^2 - (30 m/s)^2
work = 1/2 * 500 kg * (-100 m/s^2)
work = -25,000 J
The negative sign indicates that the work done is against the motion of the car. Therefore, the work done against friction is 25,000 joules.